Wallace Shawn lives in Chelsea. Meet him at a café in the neighborhood, and, making conversation while perusing the menu, ask what street he lives on, and he will begin smiling that gleeful, rueful, slightly malevolent smile that, along with his bouncing, perpetually astonished, faintly lisping voice, makes him such an indelible comic villain on TV and in movies. Smirking madly, he will decline to name a street, explaining that his mother was a “brilliant woman” with “too much emotional energy to devote to her children,” and as a result he is quite secretive.

O.K., nevermind where he lives. Let’s talk more about his mother, Cecille, a journalist who gave up her career to raise Mr. Shawn and his siblings. “Her name was not in the paper, and she didn’t have an impressive job description, so as far we knew she was a rather silly person who just went shopping all day and would come back from Bonwit Teller or B. Altman with a hat box with a hat in it,” Mr. Shawn says. It wasn’t until he was an adult that he realized his mother was “a very profound person, incredibly shrewd and intelligent,” which the actor only discovered when his father died and he had conversations alone with his mother.

Conversations about…?

Mr. Shawn, who has by this point ordered an orange juice and put on a sweater to combat the air conditioning in the café, smiles ever more violently. “I haven’t, I’m sorry to say, followed all the twists and turns of TheNew York Observer, but they’ve written thousands of columns about my family,” he says. “I’m happy to discuss my personality but I don’t want to add to TheNew York Observer log about the Shawns.”

Oh, boy. Perhaps we should start again. Let’s discuss The Master Builder, the Ibsen play that Mr. Shawn spent 15 years translating from the Norwegian (despite not speaking the language) and is now releasing as a film, directed by Jonathan Demme, with Mr. Shawn in the lead role. The voice deepens and slows, and the actor becomes both earnest and amiable. He’s stopped smiling, but he’s a lot more content.

“It’s a mystery to me why he’s not more appreciated,” says his Builder costar Julie Hagerty, who has also appeared in his play The Designated Mourner. “When people discover him it’s like discovering the moon.”

Such is the burden of being Wallace Shawn. To publishing gossips he is famous for being the son of William Shawn, whose 35-year tenure helming the New Yorker made him quite possibly the most legendary magazine editor of the 20th century, a man whose professional decorum belied a complicated family life including a decades-long affair with his employee, Lillian Ross. To consumers of popular culture Wallace Shawn is the comic foil in dozens of commercial films and TV shows (Star Trek, Toy Story, Gossip Girl and The Princess Bride, to name just a few.) But his plays are what he really wants to be known for, which, he has claimed, only two other people in the world like. “It’s a mystery to me why he’s not more appreciated,” says his Builder costar Julie Hagerty, who has also appeared in his play The Designated Mourner. “When people discover him it’s like discovering the moon.”

“I’m bourgeois to the roots,” he says, but he’s also a passionate leftist who no longer reads the New Yorker because he finds its politics too centrist. (Photos by Rick Wenner)

Depending on how you look at it, Mr. Shawn is either one of the most fortunate actors on the planet (described as a “homunculus” by Woody Allen’s character in Mr. Shawn’s first film appearance, Manhattan, in which he played Diane Keaton’s unlikely sexual lothario first husband, he has neither movie star looks nor voice, yet has enjoyed an enviable film career) or an unappreciated artistic genius, doomed to be misinterpreted as, in his own words, a “show business clown.” (His longtime collaborator, the director Andre Gregory, says Mr. Shawn is not only “America’s greatest writer,” but also a “deeply serious actor” who would make an excellent Lear or Willie Loman.) How does Mr. Shawn himself see it? A little bit of both.

In A Master Builder (Mr. Shawn changed the title from The to A) he plays Halvard Solness, an architect who has clawed his way to success over the backs of his former partner and his wife (who, like Cecille Shawn, is a study in thwarted ambitions.) Near the end of his career he is visited by Hilde, a mercurial young woman who claims Solness kissed her when she was a young girl and promised her a kingdom, and has now arrived to collect. In translating the text, Mr. Shawn not only updated the language for a contemporary production, he set the action on Solness’ death bed, so that Hilde’s visit, and all that it brings about, now reads as a fever dream. “The dream makes a lot of sense of Hilde, but it also interprets the play as Solness feeling sick of being such a horrible person and trying to think through the themes of his life,” Mr. Shawn says. “He can’t resolve all the contradictions of his life, and he dies trying, so to speak.”

Like Solness, Mr. Shawn is filled with contradictions, some possibly irreconcilable. He uses the term bourgeois to describe himself as easily and often as someone else might refer to their religion or vegetarianism—it seems in his mind to be an insoluble fact of his being. “I’m bourgeois to the roots,” he says, but he’s also a passionate leftist who no longer reads the New Yorker because he finds its politics too centrist. He just returned from a conference on socialism. In The Designated Mourner he derides popular culture as the drug that keeps us complacent about the world’s inequities. But popular culture has provided him the living that enables him to continue writing experimental plays, and doing passion projects like A Master Builder.

“A hostile person could say, ‘He denounces the status quo, but the films he’s been in either support or could not be seen as denunciations of the status quo,’” he says. And while the absurdity of his double life does strike him from time to time (“I was recently in a children’s movie, and I was lying on the floor with a dog on my chest doing various things and I was thinking, well, how many people who have written for The Nation have also been lying on the ground with the dog jumping all over them?”) he avoids projects that directly conflict with his beliefs: “I’ve mostly weaseled my way out of doing things that were nauseating to me. I’ve had good luck in escaping some horrible dilemmas.”

Mr. Shawn grew up on the Upper East Side, attending Dalton, where, he says, “they were trying to nurture the children and help them have high self-esteem and see what they were interested in. It was a very gentle atmosphere.” But summers were spent at a series of summer camps, one in particular where the World War II vet counselors regaled their young charges with tales of torturing and killing prisoners of war. “They described it in such a lighthearted way that it was decades later I understood what they had actually told me,” he says. “I wouldn’t have been capable of understanding that somebody was telling me what they thought was a funny story, but if you really listened to what they were saying they were talking about unspeakable crimes against fellow human beings.”

The disconnect between what a person says and the manner in which he says it is a theme Mr. Shawn would later develop when he started writing plays, as the narrators of works such as Mourner, and Aunt Dan and Lemon, which explores fascism, are perfectly likeable people speaking of appalling subjects in the most lighthearted way. “I think I am misleading people that way in most of my plays,” Mr. Shawn says. “I am a cheerful camp counselor telling an amusing story, and it’s up to the person in the audience to hear what’s actually being described.”

Mr. Shawn majored in history at Harvard, with thoughts of pursuing “factual writing.” For his thesis he profiled a local postal worker, who had a heart attack after Mr. Shawn interviewed him but lived. He then spent a year teaching in India, where he also interviewed a postal worker. This time the man died. “I took the full measure of the fact that factual writing involves getting involved with other people and … it’s disturbing,” he says. His younger brother, the composer Allen Shawn, has written two memoirs, one about his phobias, and a second about his autistic, mentally disabled twin sister Mary, who was institutionalized when she and Allen were 8 and Wallace was 13. Mr. Shawn, who lives with the fiction writer Deborah Eisenberg, expresses deep admiration for his brother’s writing: “He’s said the things I would have wanted to say about the things we both know.”

The actor spent time at Oxford, in part to avoid the draft, and wrote his first play for a competition. He was “disappointed and shocked” when it failed to win. Back in the States he taught Latin at The Day School (now Trevor Day School) on the Upper East Side, while continuing to write plays, and continuing to be rejected. After seeing Andre Gregory’s production of Alice in Wonderland he gave the director a “big, heavy envelope” of his work (“I gave that envelope to a lot of people. Usually that was the last I heard of it.”) Mr. Shawn wrote his first play to be produced, Our Late Night, for Mr. Gregory’s company, and a partnership was born.

Our Late Night is a sexually explicit, surrealist fantasy that divided audiences when it was staged at The Public Theater in 1975 (some nights they booed; one night they even mooed.) It won an Obie, but, Mr. Shawn says, he made about $400 for the play. In the meantime he had appeared in a stage production of The Mandrake, which he translated, and that led to movie roles, starting with Manhattan in 1979, followed by the surprise hit My Dinner with Andre, which consists entirely of Mr. Shawn and Mr. Gregory’s wide-ranging conversation over the course of a meal. He’s appeared in at least one movie nearly every year since, including many children’s films. “I’ve occasionally seen a little family sitting in the audience about to see one of my plays, and I know exactly why they’ve come,” he says. “They thought I was the amusing guy from the movies and that this play would be like the movies, and I have actually gone up to them and said, ‘I don’t think this play is going to be what you think it’s going to be.’”

Mr. Shawn says he loves acting—he mentions passing a movie shoot on the way to the café and wanting to offer his services— but is also clear-eyed about the freedom it gives him to not have to choose between being a playwright and paying the rent. “There are certain people who have said to themselves, ‘I want to do artistic work and I am prepared to live in a poor neighborhood in a shabby apartment with possibly the heating not working, eating in cheap cafeterias, never going to an expensive or good restaurant, not eating fresh vegetables but eating vegetables that are frozen,’” he says. “Because I became an actor, and I became relatively successful, nobody ever hit me with the decision, either you’re going to live in a slum or you’ve got to change your profession. I really never suffered for my life as an artistic person.”

Yet much of his writing directly challenges what he sees as the insidiousness of a social system that enables self-defined liberals to choose comfort and complacency over outrage and action. So how does he reconcile this contradiction in his own life? “I crossed the line at a certain point in my early 40s, after which the contradictions in my life couldn’t be resolved,” he says. “I would say that once you perceive the injustice of the status quo, you can’t really go back from that. No matter how much fun I might be having in one way or another, there’s an awareness hovering right in front of me that I am a beneficiary of an unjust system.”

While he doesn’t believe his plays constitute a form of social protest (“I wish!” he barks), he does try to atone for his own privilege. In January he mounted a one-night-only production of The Designated Mourner in Brazil for the journalist Glenn Greenwald, who published Edward Snowden’s leaked NSA documents and feared detention if he returned to the U.S. “Here is someone who’s done something I admire, and I can express solidarity with him and tell the powers that be how I feel, and that was a kind of liberating moment,” Mr. Shawn says. “But I wouldn’t know how to write a play that was planned to be beneficial or to make a socially worthwhile point.”

It is possible, also, that the contradictions in Mr. Shawn’s life are too useful for him to resolve. In his acting, he remains the cheerful camp counselor, playing his villains as more ingratiating than menacing. Even made up to resemble an intergalactic Mr. Potato Head as the rapacious, misogynistic Grand Nagus on Star Trek: Deep Space Nine, he exudes that unmistakable Shawnian glee. “This is a national characteristic,” he says. “Even our political leaders are very agreeable, but then you read the cold facts about what has been done and somehow they’ve managed to be cold-blooded murderers at the same time. It’s a fascinating paradox I’ve explored as a writer and an actor.”

Towards the end of our breakfast the waitress interrupts to ask how Mr. Shawn likes his egg and chive scramble. “It’s outstandingly great!” he says, with that same amazed, almost incredulous enthusiasm. But, he claims, his nature is dark. “He’s amazing at expressing true rage,” says Mr. Gregory. “Not an imitation of rage, but the thing itself.” Master builder Solness is incandescent with rage, though Mr. Shawn’s interpretation grins and guffaws through much of the play. “One of the fascinating things about being an actor is that you get to really show the vile parts of yourself that you conceal in daily life,” he says. “For instance in A Master Builder, it’s not just playing around. That’s a side of me. That’s a picture of me, except that I don’t act like that in real life because I’ve prevented myself from acting like that.”

As we leave the café, a woman accosts Mr. Shawn with her phone, wanting to take a selfie for her “wall of no-shame.” Instantly genial, the actor poses graciously, then emerges onto the street looking a bit dazed. “Isn’t that incredible?” he muses. It is unclear if he is delighted at being recognized, outraged by the imposition, or just in awe of the clarity of resolution on her phone’s camera. He is, of course, smiling like a madman, so it’s impossible to say.